7.3: Exercises
( \newcommand{\kernel}{\mathrm{null}\,}\)
Use the horizontal line test to determine if the function is one-to-one.
- f(x)=x2+2x+5
- f(x)=x2−14x+29
- f(x)=x3−5x2
- f(x)=x2x2−3
- f(x)=√x+2
- f(x)=√|x+2|
- Answer
-
- no (that is: the function is not one-to-one)
- yes
- no
- no
- no
- no
- yes
- no
Find the inverse of the function f and check your solution.
- f(x)=4x+9
- f(x)=−8x−3
- f(x)=√x+8
- f(x)=√3x+7
- f(x)=6⋅√−x−2
- f(x)=x3
- f(x)=(2x+5)3
- f(x)=2⋅x3+5
- f(x)=1x
- f(x)=1x−1
- f(x)=1√x−2
- f(x)=−54−x
- f(x)=xx+2
- f(x)=3xx−6
- f(x)=x+2x+3
- f(x)=7−xx−5
- f given by the table: x24681012f(x)371852
- Answer
-
- f−1(x)=x−94
- f−1(x)=−x+38
- f−1(x)=x2−8
- f−1(x)=x2−73
- f−1(x)=−(x6)2−2=−x2−7236
- f−1(x)=3√x
- f−1(x)=3√x−52
- f−1(x)=3√x−52
- f−1(x)=1x+1=1+xx
- f−1(x)=(1x)2+2=1+2x2x2
- f−1(x)=5y+4=5+4yy
- f−1(x)=5y+4=5+4yy
- f−1(x)=2x1−x
- f−1(x)=6xx−3
- f−1(x)=2−3xx−1
- f−1(x)=5x+7x+1
- x371852f−1(x)24681012
Restrict the domain of the function f in such a way that f becomes a one-to-one function. Find the inverse of f with the restricted domain.
- f(x)=x2
- f(x)=(x+5)2+1
- f(x)=|x|
- f(x)=|x−4|−2
- f(x)=1x2
- f(x)=−3(x+7)2
- f(x)=x4
- f(x)=(x−3)410
- Answer
-
- restricting to the domain D=[0,∞) gives the inverse f−1(x)=√x
- restricting to the domain D=[−5,∞) gives the inverse f−1(x)=√x−1−5
- restricting to the domain D=[0,∞) gives the inverse f−1(x)=x
- restricting to the domain D=[4,∞) gives the inverse f−1(x)=x+6
- restricting to the domain D=[0,∞) gives the inverse f−1(x)=√1x
- restricting to the domain D=[−7,∞) gives the inverse f−1(x)=√−3x−7
- restricting to the domain D=[0,∞) gives the inverse f−1(x)=4√x
- restricting to the domain D=[3,∞) gives the inverse f−1(x)=3+4√10x
Determine whether the following functions f and g are inverse to each other.
- \(f(x)=x+3, \quad g(x)=x-3\),
- f(x)=−x−4,g(x)=4−x,
- f(x)=2x+3,g(x)=x−32,
- f(x)=6x−1,g(x)=x+16,
- f(x)=x3−5,g(x)=5+3√x,
- f(x)=1x−2,g(x)=1x+2.
- Answer
-
- yes (that is: the functions f and g are inverses of each other)
- no
- no
- yes
- no
- yes
Draw the graph of the inverse of the function given below.
- f(x)=√x
- f(x)=x3−4
- f(x)=2x−4
- f(x)=2x
- f(x)=1x−2 for x>2
- f(x)=1x−2 for x<2
- Answer
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